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A compound microscope is an instrument that consists of two lenses L1 and L2. The lens L1 called objective forms a real, inverted and magnified image of the given object. This serves as the object for the second lens L2; the eyepiece. The eyepiece functions as a simple microscope or magnifier. It produces the final image, which is inverted with respect to the original object, enlarged and virtual.

If the power of the eyepiece (L2) is 5 diopters and it forms an image at a distance of 80 cm from its optical centre, at what distance should the object be?

  1. 12 cm
  2. 16 cm
  3. 18 cm
  4. 20 cm

Refraction Lens

Answer

16 cm

Reason — Given,

Power = +5D [convex lens has positive sign]

v = -80 cm.

u = ?

From formula,

P = 100f(cm)\dfrac{100}{\text{f(cm)}}

Substituting we get,

5 = 100f\dfrac{100}{f}

f = 1005\dfrac{100}{5} = 20 cm

Using formula,

1f\dfrac{1}{\text{f}} = 1v\dfrac{1}{\text{v}} - 1u\dfrac{1}{\text{u}}

We get,

120\dfrac{1}{\text{20}} = 1-80\dfrac{1}{\text{-80}} - 1u\dfrac{1}{\text{u}}

1u\dfrac{1}{\text{u}} = -180\dfrac{1}{\text{80}} - 120\dfrac{1}{\text{20}}

1u\dfrac{1}{\text{u}} = −1−480\dfrac{-1-4}{\text{80}} = −580\dfrac{-5}{\text{80}}

1u\dfrac{1}{\text{u}} = −116-\dfrac{1}{\text{16}}

u = -16

Hence, distance of the object from the lens = 16 cm.

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